Details

analyze2.7s (20.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample203.0ms (1.5%)

Algorithm

1×

intervals

Results

143.0ms	158×	body	1024	valid
25.0ms	39×	body	512	valid
9.0ms	5×	body	2048	valid
6.0ms	17×	body	256	valid
6.0ms	37×	body	128	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify110.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	385	39
1	385	39

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 9.9b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
1.7b	(sin.f64 (-.f64 lambda1 lambda2))
1.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464` `pow1_binary64_1503`
9×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`associate-r_binary64_1382` `cancel-sign-sub-inv_binary64_1408`
4×	`sin-sum_binary64_1575` `cbrt-unprod_binary64_1475` `associate-l_binary64_1383` `pow-prod-down_binary64_1513` `add-log-exp_binary64_1481` `prod-exp_binary64_1491` `cos-sum_binary64_1576`
3×	`cos-diff_binary64_1579`
2×	`sub-neg_binary64_1435` `*-commutative_binary64_1373` `sin-cos-mult_binary64_1598`
1×	`sin-diff_binary64_1578` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `associate-*l/_binary64_1385` `unswap-sqr_binary64_1410`

Counts

4 → 64

Calls

4 calls:

9.0ms	(cos.f64 (-.f64 lambda1 lambda2))
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

series207.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
52.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
20.0ms	(sin.f64 (-.f64 lambda1 lambda2))
17.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify78.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5077	1051

prune103.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	10	77

Merged error: 4.6b

Counts

77 → 10

Compiler

Compiled 2508 to 518 computations (79.3% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.1b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
1.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1464`
13×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
10×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`associate-r_binary64_1382`
7×	`associate-l_binary64_1383`
5×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
4×	`add-log-exp_binary64_1481` `cos-sum_binary64_1576`
3×	`cancel-sign-sub-inv_binary64_1408` `*-commutative_binary64_1373` `cos-diff_binary64_1579`
2×	`sin-cos-mult_binary64_1598` `unswap-sqr_binary64_1410`
1×	`sub-neg_binary64_1435` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `associate-*l/_binary64_1385`

Counts

4 → 70

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series207.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
37.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
37.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify119.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4830	1103
1	4830	1103

prune113.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Merged error: 0.0b

Counts

92 → 10

Compiler

Compiled 3266 to 580 computations (82.2% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.1b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_1464`
15×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
12×	`associate-r_binary64_1382`
11×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
10×	`associate-l_binary64_1383`
6×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
5×	`sin-cos-mult_binary64_1598`
4×	`*-commutative_binary64_1373` `add-log-exp_binary64_1481`
3×	`associate-*r/_binary64_1384` `frac-times_binary64_1452` `sin-mult_binary64_1597` `unswap-sqr_binary64_1410`
2×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450` `cos-mult_binary64_1596`
1×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `associate-*l/_binary64_1385`

Counts

4 → 83

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

series320.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

207.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
40.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
36.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
36.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5026	1744

prune151.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 0.0b

Counts

105 → 10

Compiler

Compiled 4607 to 734 computations (84.1% saved)

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(cbrt.f64 (cos.f64 lambda2))
0.2b	(cbrt.f64 (cos.f64 lambda2))
0.2b	(cbrt.f64 (cos.f64 lambda2))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_1478` `cbrt-prod_binary64_1473` `add-exp-log_binary64_1480` `pow1_binary64_1503`
8×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481` `sin-cos-mult_binary64_1598`
3×	`associate-r/_binary64_1384` `associate-r*_binary64_1382` `cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `frac-times_binary64_1452` `pow1/3_binary64_1524` `prod-exp_binary64_1491`
2×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450` `cos-mult_binary64_1596` `sin-mult_binary64_1597`
1×	`associate-l_binary64_1383` `-commutative_binary64_1373` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `associate-l/_binary64_1385`

Counts

4 → 60

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
1.0ms	(cbrt.f64 (cos.f64 lambda2))
1.0ms	(cbrt.f64 (cos.f64 lambda2))
1.0ms	(cbrt.f64 (cos.f64 lambda2))

series401.0ms (3%)

Counts

4 → 12

Calls

4 calls:

196.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
71.0ms	(cbrt.f64 (cos.f64 lambda2))
69.0ms	(cbrt.f64 (cos.f64 lambda2))
65.0ms	(cbrt.f64 (cos.f64 lambda2))

simplify102.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4949	1398
1	4949	1398

prune98.0ms (0.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	72	10	82

Merged error: 0.0b

Counts

82 → 10

Compiler

Compiled 3831 to 427 computations (88.9% saved)

regimes522.0ms (3.9%)

Compiler: Compiled 6931 to 4496 computations (35.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	128	67
1	128	67

end0.0ms (0%)

sample7.5s (56.9%)

Algorithm

1×

intervals

Results

4.9s	5296×	body	1024	valid
760.0ms	1324×	body	512	valid
348.0ms	186×	body	2048	valid
146.0ms	414×	body	256	valid
132.0ms	780×	body	128	valid

Compiler

Compiled 1135 to 736 computations (35.2% saved)

Details

analyze2.7s (20.1%)

sample203.0ms (1.5%)

simplify110.0ms (0.8%)

prune3.0ms (0%)

localize20.0ms (0.2%)

rewrite33.0ms (0.2%)

series207.0ms (1.6%)

simplify78.0ms (0.6%)

prune103.0ms (0.8%)

localize27.0ms (0.2%)

rewrite29.0ms (0.2%)

series207.0ms (1.6%)

simplify119.0ms (0.9%)

prune113.0ms (0.9%)

localize28.0ms (0.2%)

rewrite40.0ms (0.3%)

series320.0ms (2.4%)

simplify73.0ms (0.6%)

prune151.0ms (1.1%)

localize36.0ms (0.3%)

rewrite24.0ms (0.2%)

series401.0ms (3%)

simplify102.0ms (0.8%)

prune98.0ms (0.7%)

regimes522.0ms (3.9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.5s (56.9%)

Profiling